c-AFM measures a current in contact mode running through your tip into the sample and into some form of back contact. You always need a closed circuit. Depending on the choice of back contact and geometry, you might even measure different things of your sample.

Typically the back contact is the substrate, which is connected with the sample holder. If it is not contacted, you are measuring the current through the (insulating) substrate, which is dominated by the resistance of the substrate.

In your case, if your few layers thick graphene flake sits on a homogeneous gold substrate, even after contacting the gold surface, you might not measure anything useful about the flake, because the current will just bypass your flake and you just measure the sheet resistance of the gold flake. You need to think of the possible current pathways, when interpreting your data or setting up such an experiment. Depending on your research question, you might want to put the graphene flake on an insulating substrate and doing the back contact by some form of bonding or localized gold evaporation only.